- #26

- 107

- 4

I read and reread Matt arguments trying to understand his viewpoints. I think he got discouraged with the LHC non-null results in 2013.. and he wrote in separate page in August 2013 https://profmattstrassler.com/2013/08/27/a-first-stab-at-explaining-naturalness/The problem with this folklore story is that it is trying to nail jelly to the wall by arguing about the size of quantum corrections in the presence of renormalization freedom.

The fact of the matter is that the space of renormalization choices is an affine space (i.e. like a vector space, but with no origin singled out) which means first of all that there is no absolute concept of "size" of a quantum correction. This only appears once one fixes a renormalization scheme, which is like a choice of coordinate chart. It has no physical meaning. Even if we fix a renormalization scheme (which is implicitly assumed in discussions such as you quote) then it still remains a fact that there is an arbitrary freedom in choosing renormalization constants, large or not.

In conclusion, to make progress on these kinds of matters, one needs more theoretical input than just low energy effective perturbative quantum field theory with its arbitrary renormalization freedom, or otherwise one is going in circles forever. As Kane 17 points out, "we should look harder for a theory that does provide a UV-completion".

Notice how the solution of the hierarchy problem observed by Acharya-Kane-Kumar 12, section V.A.2 (p. 10-11) deals with this issue: They invoke a UV-completion that goes beyond perturbation theory. In that theory one knows 1) that the superpotential is protected against perturbative renormalization freedom and 2) the form of the non-perturbative corrections is known. Namely these are exponentials in the inverse coupling. This yields the exponential hierarchy that is to be explained.

You see, this works not by long story-telling and analogies and showing colorful pictures, but by a logical deduction from a theoretical framework.

(Not fully mathematically rigorous, but fairly solid by the standards of phenomenology.)

"This in turn is why so many particle physicists have long expected the LHC to discover more than just a single Higgs particle and nothing else… more than just the Standard Model’s one and only missing piece… and why it will be a profound discovery with far-reaching implications if, during the next five years or so, the LHC experts sweep the floor clean and find nothing more in the LHC’s data than

__the Higgs particle that was found in 2012__."

It's happening now.. it's 5 years from his pronouncement. Only Higgs and nothing else is "Profound discovery with far-reaching implications". There is possibility there may not even be a UV complete theory. To be on topic, where is Matt page about Vacuum Metastability? He should emphasize it too.

Anyway. If AdS/CFT is UV complete. But it doesn't describe our spacetime. Is this duality just toy model or does it completely describe a hidden sector that can act as holographic surface. Is there any reference about this search for actual surface or it will remain as toy model for centuries to come? And can AdS/CFT explain the why of the vacuum metastability?